{"title":"一类由混合局部-非局部算子驱动的椭圆型问题","authors":"Zijian Wu, Haibo Chen","doi":"10.1080/17476933.2023.2266689","DOIUrl":null,"url":null,"abstract":"AbstractIn this paper, we consider a class of elliptic problems driven by a mixed local-nonlocal operator. By estimating the critical groups and using Morse theory, the existence of nontrivial solutions is obtained in different cases. Our results extend some classical theorems for semilinear elliptic equations to the mixed local-nonlocal setting.Keywords: Nontrivial solutionssemilinear elliptic problemscritical groupsMorse theoryAMS Subject Classifications: 35J6035J91 AcknowledgementThe authors are grateful to the anonymous referees for their useful comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementDate sharing is not applicable to this article as no new data were created or analysed in this study.","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A class of elliptic problems driven by a mixed local-nonlocal operator\",\"authors\":\"Zijian Wu, Haibo Chen\",\"doi\":\"10.1080/17476933.2023.2266689\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"AbstractIn this paper, we consider a class of elliptic problems driven by a mixed local-nonlocal operator. By estimating the critical groups and using Morse theory, the existence of nontrivial solutions is obtained in different cases. Our results extend some classical theorems for semilinear elliptic equations to the mixed local-nonlocal setting.Keywords: Nontrivial solutionssemilinear elliptic problemscritical groupsMorse theoryAMS Subject Classifications: 35J6035J91 AcknowledgementThe authors are grateful to the anonymous referees for their useful comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementDate sharing is not applicable to this article as no new data were created or analysed in this study.\",\"PeriodicalId\":51229,\"journal\":{\"name\":\"Complex Variables and Elliptic Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-10-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Variables and Elliptic Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/17476933.2023.2266689\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Variables and Elliptic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/17476933.2023.2266689","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A class of elliptic problems driven by a mixed local-nonlocal operator
AbstractIn this paper, we consider a class of elliptic problems driven by a mixed local-nonlocal operator. By estimating the critical groups and using Morse theory, the existence of nontrivial solutions is obtained in different cases. Our results extend some classical theorems for semilinear elliptic equations to the mixed local-nonlocal setting.Keywords: Nontrivial solutionssemilinear elliptic problemscritical groupsMorse theoryAMS Subject Classifications: 35J6035J91 AcknowledgementThe authors are grateful to the anonymous referees for their useful comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementDate sharing is not applicable to this article as no new data were created or analysed in this study.
期刊介绍：
Complex Variables and Elliptic Equations is devoted to complex variables and elliptic equations including linear and nonlinear equations and systems, function theoretical methods and applications, functional analytic, topological and variational methods, spectral theory, sub-elliptic and hypoelliptic equations, multivariable complex analysis and analysis on Lie groups, homogeneous spaces and CR-manifolds.
The Journal was formally published as Complex Variables Theory and Application.
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